The (projective) Lehrenfeld-Schölberl stabilization function

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1

Hi,

I’m trying to implement an HDG method with reduced stabilization for second-order diffusion problems. Precisely, I want to use the (projective) Lehrenfeld-Schöberl stabilization function.

Is this function already available in NGSolve, or should I create it?

Regards,
Gregory

2

Hi Gregory,

It’s available in NGSolve. Attached is a minimal example. You may also want to have a look at the documentation of FacetFESpace. To do so type

help(FacetFESpace). The key is the two flag

highest_order_dc

and

hide_highest_order_dc

which do the projected-jumps trick as explained in 2.2.2. in this (preprint version of the ) paper: https://arxiv.org/pdf/1508.04245.pdf . For the even more basic stuff about HDG in NGSolve I refer you to the i-tutorial 2.8, see
https://ngsolve.org/media/kunena/attachments/743/hdg.pyhttps://ngsolve.org/docu/latest/i-tutorials/unit-2.8-DG/DG.html .

Best,
Christoph

Attachment: hdg.py

3

Hi Christoph,

Thank you for your response.
I follow the same steps for the FESpace as in the attached script. In the function, I have set “highest_order_dc = true” and “hide_highest_order_dc = True”.
Now it works fine.

Thanks,
Gregory